State Feedback Trajectory Tracking Control of Nonlinear Affine in Control System with Unknown Internal Dynamics and Disturbances

In this paper, a new state adaptive optimal nonlinear control is presented for the realization of the trajectory tracking of nonlinear affine-in control systems with unknown internal dynamics and disturbances. This proposed optimal controller which is developed in four steps is on the basis of a L-2 norm prescribed to minimize the trajectory tracking error between the desired state reference and its state feedback, and a time-delay estimation technique used for the estimation of the nonlinear unknown internal dynamics and disturbances. Because of the application of the time-delay estimation technique, the entire proposed controller has both the adaptive and optimal characteristics. With the systems state feedback, the proposed controller which doesn't require any knowledge of nonlinear internal dynamics and disturbances ensures the state trajectory tracking. Finally, to validate and demonstrate the performance of this proposed method, a satellite numerical example with comparisons to classical Proportional Integral-Derivative Controller is used to illustrate the proposed controller performance and effectiveness.